You dropped your spindle or you are ready to attach new fiber – no problem.
On the spun side, leave a bit of fuzzy fiber (not yet spun or take out twist if you need to) about 1 inch. The fiber source should also be fuzzy. Overlap the two pieces by a little less than an inch. Make sure you have the tips of the spindle side fiber in your fiber hand grasp. You will need to hold them together until you get twist in there.
Hold fiber, get your spindle going again with gently twist, draft your fiber.
note: You will need enough time deal with drafting the overlap fiber connection area so go a little slow on the amount of twist until you get the fiber drafted evenly and securely connected again.
If it turns out the fiber is to thick at the connection, park your spindle, (while holding the yarn on either side of the connection area) loosen the twist with your spindle hand by rolling the yarn in the opposite directions of the twist. While holding back that twist, pull apart (draft) at that connection point in super small increments until you are satisfied with the thickness. Let the twist you were holding back back into the fiber.
note: If you can’t draft apart, you either need to untwist more or move your hands a little further apart (remember staple length).